Improvements are presented to the prior-art in the field of sliding pendulum seismic isolation systems.
The prior-art sliding pendulum bearings employ concave spherical or cylindrical surfaces, and sliders, which slide along these concave surfaces, resulting in a lifting of the supported structure during seismic ground motions. The lifting of the structure results in an equivalent pendulum motion. The radii of curvature of the concave surfaces result in an effective length of the pendulum arm, that determines the dynamic natural period of vibration of the isolation system. The friction, which occurs between the sliders and the concave surfaces, serves the important function of dissipating the energy associated with the seismic movements, that determines the effective friction and equivalent viscous damping of the isolation system.
A typical sliding pendulum seismic isolation system would employ three or more sliding pendulum bearings to support a structure and protect it from earthquake ground motions. The sliding pendulum mechanisms of these bearings are connected in parallel by the structure. For a pure horizontal displacement of the structure, the displacement occurring in each sliding pendulum mechanism is substantially equal to the displacement of the structure in that direction.
The prior-art spherical pendulum isolation systems are configured such that all sliders would slide in substantial unison during seismic movements, resulting in one effective pendulum length, and having one dynamic natural period of vibration based on pendulum type motion. The dynamic natural period of vibration of the isolation system (T) is equal to:T=2π(L/g)1/2 
Where L is the effective pendulum length, g is the acceleration of gravity, and π is equal to 3.1414.
The average friction occurring between the sliders and the concave surfaces determines the effective dynamic friction for the isolation system. The prior-art spherical bearings are configured such that the dynamic natural period and the effective friction is the same for sliding motion occurring in any horizontal direction. The prior-art spherical bearings are configured such that the effective friction is the same for different amplitudes of sliding motion.
The prior-art cylindrical pendulum systems operate similar to the spherical pendulum systems, except they have two independent sliding pendulum mechanisms operating in perpendicular directions. Each direction has a dynamic natural period according to the above equation. Each direction has an effective friction determined from the average friction of the sliders operating in that direction. Each direction has an effective friction that is the same for different amplitudes of sliding motion in that direction.
For both spherical and cylindrical sliding pendulum mechanisms, for lateral movements of the supported structure, the energy dissipated through friction in the bearings is in direct linear proportion to the total cumulative displacement travel of the supported structure. For one symmetrical cycle of movement of the supported structure, the energy dissipated per cycle (“EDC”) is equal to:EDC=4Wfeffd 
Where W is the weight of the supported structure, feff is the effective friction of the isolation system, and d is the displacement amplitude away from, and back to center, in both the positive and negative directions. The EDC increases in direct proportion to increases in the displacement amplitude, d. The EDC also increases in direct proportion to increases in the effective friction. The EDC is used to calculate the equivalent viscous damping percentage, for cycles having a specified amplitude of lateral displacement. As the EDC increases, the equivalent viscous damping percentage increases.
In the typical seismic design of a structure supported by the prior-art systems, the strength of the structural frame would be designed to resist the seismic forces expected to occur during the design level earthquake. The effective pendulum length and effective friction of the bearings would be selected to achieve the target seismic forces during the design level earthquake. The design level earthquake is a strong earthquake having a reasonable probability of occurring once during the life of the structure. Lower strength service level earthquakes would be expected to occur more than once during the life of the structure. As compared to bearings designed specifically to minimize impacts from service level earthquakes, the prior-art bearings designed for the stronger design level earthquake would be considerably less effective at protecting contents and architectural components during service level earthquakes. Also, building codes typically require the bearings to accommodate the displacements that would occur during a maximum credible earthquake. These displacements are typically 50% to 100% larger than the design level earthquake displacements. Accommodating these larger displacements adds substantial cost to both the bearings and the structure seismic gaps.
The improvements to the prior-art sliding pendulum systems presented herein do not pertain to seismic isolation systems which employ rubber or steel springs as the primary means to achieve the desired isolation system period, nor to seismic isolation systems which employ fluid or viscous dampers as the primary means of dissipating the seismic motion energy, nor to energy dissipation devices that do not support a structure load, nor to sliding isolation systems which employ flat sliders and separate elements to provide the restoring force or damping, nor to negative pendulum systems which employ sliders sliding along convex surfaces resulting in a lowering of the supported structure, nor to isolation systems which employ roller bearings or rocker bearings to achieve equivalent pendulum motion, nor to sliding isolation systems which employ sliding mechanisms having sliders that for a substantive portion of their sliding distance slide along concave surfaces that are neither spherical nor cylindrical.
More that 95% of the prior-art patents for seismic bearings or supports have never been implemented in actual structures because of the high costs associated with their implementation. Although the majority of these prior-art bearings can be very effective at reducing seismic forces acting on the supported structures, if they are not cost-effective, they are never used. A major objective of the inventive method presented below is to achieve a cost-effective seismic isolation system.